The ring of multisymmetric functions

2004/05/26 by F. Vaccarino, Vaccarino, F.
Mathematics · #05E05 #13A50 #20C30 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #math.AC #math.CO #math.RT #msc:05E05 #msc:13A50 #msc:20C30

paper · pdf · doi:10.48550/arxiv.math/0405490

to be published on Annales de l'Institut Fourier vol.55 (2005)

arxiv created 2005/03/24 · arxiv updated 2009/12/01

Abstract

Let R be a commutative ring and let n,m be two positive integers. The symmetric group on n letters acts diagonally on the ring of polynomials in nxm variables with coefficients in R. The subrings of invariants for this action is called the ring of multisymmetric functions since these are the usual symmetric functions when m=1. In this paper we will give a presentation in terms of generators and relations that holds for any R and any n,m answering in this way to a classical question. I would like to thank M.Brion, C.De Concini and C.Procesi, in alphabetical order, for useful discussions.

Related

• The ring of multisymmetric functions
• Symmetric products, linear representations and the commuting scheme
• Splitting algebras, Symmetric functions and Galois Theory
• Applications of multisymmetric syzygies in invariant theory
• Explicit polynomial generators for the ring of quasi-symmetric functions over the integers